Iain Duncan Smith's department will only be able to make further savings using radical measures, the review says. Photograph: Richard Kaminski/Rex

The government's ambitious welfare reform strategy is at risk because of the speed and depth of the cuts imposed on Iain Duncan Smith's work and pensions department, according to a leaked internal review.

The document reveals that the Department for Work and Pensions (DWP) is struggling to meet "extremely challenging" demands for over £1bn of efficiency savings over the next two years and these pressures could disrupt plans to roll out benefits reforms.

Too crude an approach to future cuts would affect the quality and capacity of the DWP's "public-facing" services to vulnerable pensioners, jobseekers and benefit claimants, it warns.

It is understood that separate internal DWP modelling shows that, as universal credit is expanded in the months before the general election next year, the cuts will diminish the department's capacity to keep on top of rising customer demand in jobcentres and benefit offices.

Most of the more straightforward cuts have been made over the past two years, the DWP review says, and further savings can be achieved only by radical measures, such as outsourcing core services to the private sector, investing heavily in new IT systems, and moving to digital-only customer services.

The review, carried out in tandem with the Treasury and the Cabinet Office, points out that the DWP, which is Whitehall's biggest department, has made £2bn of savings since 2009. Almost 30,000 posts (24% of the workforce) have been cut, with thousands more expected through voluntary redundancy schemes in the next few months.

The review warns, however, that future cuts of over £1bn could jeopardise the department's capacity to roll out reforms including those of pensions, child maintenance and disability benefits. The flagship universal credit programme, which is beset by delays and IT problems, is not part of the review.

It says a future cuts strategy has to take into account the quality and effectiveness of the DWP's services, not just the level of efficiency savings: "Going too far and too fast on the latter risks stymieing the former, which will in the end lead to increased overall costs and is also a risk for delivery of the department's reform agenda."

It adds: "DWP faces a massive challenge to plan in a way that allows the department to live within its spending envelope."

A DWP spokesperson said: "The department already has a track record of delivering significant reforms at the same time as achieving £2bn in efficiency savings, and we'll continue to do so. Unemployment is falling, employment is at a record high and we are reforming welfare to make sure work pays."

Ironically, the review points out that new demands from ministers have made it harder to make savings. Decisions to tighten the conditions on jobseekers by making them attend jobcentres more regularly meant many local offices earmarked for closure had to be kept open, preventing officials from making £40m of savings.

Without detailing an exact figure, it says the introduction of the claimant commitment by ministers last October – an eight-page document that jobseekers have to sign up to and renew on a regular basis – had a "significant impact" on costs.

New cost-cutting proposals include ditching paper-based form-filling and moving rapidly to an online-only approach to customer services as a way of cutting administrative costs. In time this may extend to jobcentres, under a model pioneered by the Canadian government.

The department intends to stop paying benefits into Post Office card accounts – basic cash accounts used by nearly 3 million people, including 1.5 million pensioners, many of whom do not have ordinary bank accounts. This could prove politically controversial because it would undermine the financial viability of rural post offices.

The card accounts are expensive and not flexible enough to handle universal credit benefit payments, the review says: "DWP recognise that there are wider cross-government considerations, such as maintaining the footfall and associated income in rural post offices. However, this is not for DWP to address by paying for products not needed and which for some people are not suitable."

Another potentially unpopular proposal is to make claims for attendance allowance (AA) – payments made to disabled people over 65 to help with their living costs – online only. Although just 2% of AA claims are currently done online and the claimants are more likely to be digitally excluded than average, the review says huge savings can be made, and suggests carers and friends will be able to help claimants fill in the form online.

The review says officials are scrutinising all arrangements with external private suppliers, including companies involved in the work programme, to check for potential overcharging on hundreds of millions of pounds' worth of contracts, and to examine the potential to ratchet down prices in future contracts.

The Institute for Government (IfG) thinktank, which has warned that all Whitehall departments are embarked on risky "high stakes" cuts programmes, said it was important that the DWP was planning ahead for severe cuts. "If people were not having these conversations, that would be a worry," said the IfG deputy director, Julian McCrae.

Mark Serwotka, the PCS union general secretary, said the review reflected staff fears that pensioners and vulnerable people would see services suffer as a result of cuts.

"This again gives the lie to David Cameron's pre-election claim that frontline services would be protected, and exposes the failings and cruelty of austerity. It is abundantly clear that DWP is unable to cope with these cuts and needs urgent investment to ensure sick, disabled and unemployed people get the support they need and deserve."